1. CSCI283 Fall 2005 GWU All slides from Bishop’s slide set Public Key Infrastructure (PKI)

2. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set2 Notation X  Y : { Z || W } k X,Y –X sends Y the message produced by concatenating Z and W enciphered by key k X,Y, which is shared by users X and Y A  T : { Z } k A || { W } k A,T –A sends T a message consisting of the concatenation of Z enciphered using k A, A’s key, and W enciphered using k A,T, the key shared by A and T r 1, r 2 nonces (nonrepeating random numbers)

3. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set3 Session, Interchange Keys Alice wants to send a message m to Bob She generates a random cryptographic key k s and uses it to encipher m To be used for this message only Called a session key She enciphers k s with Bob’s public key k B k B enciphers all session keys Alice uses to communicate with Bob Called an interchange key Alice sends { m } k s { k s } k B

4. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set4 Benefits Limits amount of traffic enciphered with single key –Standard practice, to decrease the amount of traffic an attacker can obtain Prevents some attacks –Example: Alice will send Bob message that is either “BUY” or “SELL”. Eve computes possible ciphertexts { “BUY” } k B and { “SELL” } k B. Eve intercepts enciphered message, compares, and gets plaintext at once

5. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set5 Classical Key Exchange (without PKI) Bootstrap problem: how do Alice, Bob begin? –Alice can’t send key to Bob in the clear! Assume trusted third party, Cathy –Alice and Cathy share secret key k A –Bob and Cathy share secret key k B Use this to exchange shared key k s

6. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set6 Simple Protocol Alice Cathy { request for shared key with Bob } k A Alice Cathy { k s } k A || { k s } k B Alice Bob { k s } k B

7. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set7 Problems How does Bob know he is talking to Alice? –Replay attack: Eve records message from Alice to Bob, later replays it; Bob may think he’s talking to Alice, but he isn’t –Session key reuse: Eve replays message from Alice to Bob, so Bob re-uses session key Protocols must provide authentication and defense against replay, these are problems even when cryptography used is asymmetric Numerous solutions, we will consider ones based on the PKI

8. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set8 Public Key Key Exchange Here interchange keys known –e A, e B Alice and Bob’s public keys known to all –d A, d B Alice and Bob’s private keys known only to owner Simple protocol –k s is desired session key Alice Bob { k s } e B

9. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set9 Problem and Solution Vulnerable to forgery or replay –Because e B known to anyone, Bob has no assurance that Alice sent message Simple fix uses Alice’s private key –k s is desired session key Alice Bob { { k s } d A } e B

10. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set10 Notes Can include message enciphered with k s Assumes Bob has Alice’s public key, and vice versa –If not, each must get it from public server –If keys not bound to identity of owner, attacker Eve can launch a man-in-the-middle attack (next slide; Cathy is public server providing public keys) Solution to this (binding identity to keys) discussed later as public key infrastructure (PKI)

11. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set11 Man-in-the-Middle Attack AliceCathy send Bob’s public key Eve Cathy send Bob’s public key Eve Cathy eBeB Alice eEeE Eve Alice Bob { k s } e E Eve Bob { k s } e B Eve intercepts request Eve intercepts message

12. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set12 Cryptographic Key Infrastructure Goal: bind identity to key Classical: not possible as all keys are shared –Use protocols to agree on a shared key (see earlier) Public key: bind identity to public key –Crucial as people will use key to communicate with principal whose identity is bound to key –Erroneous binding means no secrecy between principals –Assume principal identified by an acceptable name

13. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set13 Certificates Create token (message) containing –Identity of principal (here, Alice) –Corresponding public key –Timestamp (when issued) –Other information (perhaps identity of signer) signed by trusted authority (here, Cathy) C A = { e A || Alice || T } d C

14. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set14 Use Bob gets Alice’s certificate –If he knows Cathy’s public key, he can decipher the certificate When was certificate issued? Is the principal Alice? –Now Bob has Alice’s public key Problem: Bob needs Cathy’s public key to validate certificate –Problem pushed “up” a level –Two approaches: Merkle’s tree, signature chains

15. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set15 Merkle’s Tree Scheme Keep certificates in a file –Changing any certificate changes the file –Use crypto hash functions to detect this Define hashes recursively –h is hash function –C i is certificate i Hash of file (h(1,4) in example) known to all h(1,4) h(1,2) h(3,4) h(1,1) h(2,2) h(3,3) h(4,4) C 1 C 2 C 3 C 4

16. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set16 Validation To validate C 1 : –Compute h(1, 1) –Obtain h(2, 2) –Compute h(1, 2) –Obtain h(3, 4) –Compute h(1,4) –Compare to known h(1, 4) Need to know hashes of children of nodes on path that are not computed h(1,4) h(1,2) h(3,4) h(1,1) h(2,2) h(3,3) h(4,4) C 1 C 2 C 3 C 4

17. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set17 Problem File must be available for validation –Otherwise, can’t recompute hash at root of tree –Intermediate hashes would do Not practical in most circumstances –Too many certificates and users –Users and certificates distributed over widely separated systems

18. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set18 Certificate Signature Chains Create certificate –Generate hash of certificate –Encipher hash with issuer’s private key Validate –Obtain issuer’s public key –Decipher enciphered hash –Recompute hash from certificate and compare Problem: getting issuer’s public key

19. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set19 X.509 Chains Some certificate components in X.509v3: –Version –Serial number –Signature algorithm identifier: hash algorithm –Issuer’s name; uniquely identifies issuer –Interval of validity –Subject’s name; uniquely identifies subject –Subject’s public key –Signature: enciphered hash

20. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set20 X.509 Certificate Validation Obtain issuer’s public key –The one for the particular signature algorithm Decipher signature –Gives hash of certificate Recompute hash from certificate and compare –If they differ, there’s a problem Check interval of validity –This confirms that certificate is current

21. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set21 Issuers Certification Authority (CA): entity that issues certificates –Multiple issuers pose validation problem –Alice’s CA is Cathy; Bob’s CA is Don; how can Alice validate Bob’s certificate? –Have Cathy and Don cross-certify Each issues certificate for the other

22. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set22 Validation and Cross-Certifying Certificates: –Cathy > –Dan –Cathy > –Dan > Alice validates Bob’s certificate –Alice obtains Cathy > –Alice uses (known) public key of Cathy to validate Cathy > –Alice uses Cathy > to validate Dan >

23. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set23 PGP Chains OpenPGP certificates structured into packets –One public key packet –Zero or more signature packets Public key packet: –Version (3 or 4; 3 compatible with all versions of PGP, 4 not compatible with older versions of PGP) –Creation time –Validity period (not present in version 3) –Public key algorithm, associated parameters –Public key

24. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set24 OpenPGP Signature Packet Version 3 signature packet –Version (3) –Signature type (level of trust) –Creation time (when next fields hashed) –Signer’s key identifier (identifies key to encipher hash) –Public key algorithm (used to encipher hash) –Hash algorithm –Part of signed hash (used for quick check) –Signature (enciphered hash) Version 4 packet more complex

25. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set25 Signing Single certificate may have multiple signatures Notion of “trust” embedded in each signature –Range from “untrusted” to “ultimate trust” –Signer defines meaning of trust level (no standards!) All version 4 keys signed by subject –Called “self-signing”

26. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set26 Validating Certificates Alice needs to validate Bob’s OpenPGP cert –Does not know Fred, Giselle, or Ellen Alice gets Giselle’s cert –Knows Henry slightly, but his signature is at “casual” level of trust Alice gets Ellen’s cert –Knows Jack, so uses his cert to validate Ellen’s, then hers to validate Bob’s Bob Fred Giselle Ellen Irene Henry Jack Arrows show signatures Self signatures not shown

27. 6/3/2015CS283/Fall05/GWU/Vora/PKI All slides from Bishop's set27 Identity Based Encryption (Boneh et al) New cryptographic technique to generate public key from email address, or any identifier.